Hi,
I guess that the problem is the delayed evaluation of
$\psi$. (BTW, it is quite cumbersome to retype everything if you paste an image into your post. The code would be much easier to debug.
a[n_] := (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SuperscriptBox[\(Sin[
\*FractionBox[\(Pi\ n\), \(2\)] x]\), \(2\)] \[DifferentialD]x\)\))^-1
b[n_] := (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SuperscriptBox[\(Cos[
\*FractionBox[\(Pi\ n\), \(2\)] x]\), \(2\)] \[DifferentialD]x\)\))^-1
\[Phi]odd[x_, n_] := b[n] Cos[(Pi n)/2 x]
\[Phi]even[x_, n_] := a[n] Sin[(Pi n)/2 x]
\[Psi][x_, \[Alpha]_, \[Beta]_] := -\[Alpha] \[Phi]odd[x,
1] + \[Beta] \[Phi]even[x, 2]
As you say, if you plot
Plot[{\[Psi][x, 2^-0.5, 2^-0.5], \[Psi][x, 3^-0.5, (2/3)^-0.5]}, {x, -1, 1}]
that does not work. You can either prefix everything with Evaluate:
Plot[Evaluate@{\[Psi][x, 2^-0.5, 2^-0.5], \[Psi][x, 3^-0.5, (2/3)^-0.5]}, {x, -1, 1}]
or modify the definition of
$\psi$ like so:
\[Psi][x_, \[Alpha]_, \[Beta]_] = -\[Alpha] \[Phi]odd[x, 1] + \[Beta] \[Phi]even[x, 2]
Now, it's not a delayed definition anymore. Now the plot command works without the Evaluate.
Cheers,
Marco
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